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Formally, a Markov partition is used to provide a finite cover for the smooth system ; each set of the cover is associated with a single symbol, and the sequences of symbols result as a trajectory of the system moves from one of the covering sets to another.

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## Some Related Sentences

Formally and Markov

Formally and partition

__Formally__

**,**given

**a**

**finite**

**set**X

**,**

**a**collection C

**of**subsets

**of**X

**,**all

**of**size n

**,**has Property B if we can

__partition__X into two disjoint subsets Y

**and**Z such that every

**set**in C meets both Y

**and**Z

**.**

Formally and is

__Formally__organized vocational programs supported by federal funds allow high school students

**to**gain experience in

**a**field

**of**work which

__is__likely

**to**lead

**to**

**a**full-time job on graduation

**.**

__Formally__

**,**

**the**

**set**

**of**all context-free languages

__is__identical

**to**

**the**

**set**

**of**languages accepted by pushdown automata ( PDA ).

More rigorously

**,****the**divergence**of****a**vector field F at**a**point p__is__defined**as****the**limit**of****the**net flow**of**F across**the****smooth**boundary**of****a**three dimensional region V divided by**the**volume**of**V**as**V shrinks**to**p**.**__Formally__**,**__Formally__

**,**

**the**base

__is__known

**as**Naval Support Facility Diego Garcia (

**the**US activity ) or Permanent Joint Operating Base ( PJOB ) Diego Garcia (

**the**UK's term ).

__Formally__

**,**there

__is__

**a**clear distinction: " DFT " refers

**to**

**a**mathematical transformation or function

**,**regardless

**of**how it

__is__computed

**,**whereas " FFT " refers

**to**

**a**specific family

**of**algorithms

**for**computing DFTs

**.**

__Formally__

**,**oxidation state

__is__

**the**hypothetical charge that an atom would have if all bonds

**to**atoms

**of**different elements were 100 % ionic

**.**

__Formally__

**,**an inner product space

__is__

**a**vector space V over

**the**field together

**with**an inner product

**,**i

**.**e.,

**with**

**a**map

__Formally__

**,**if M

__is__

**a**

**set**

**,**

**the**identity function f on M

__is__defined

**to**be that function

**with**domain

**and**codomain M which satisfies

*

__Formally__**,**when working over**the**reals**,****as**here**,**this__is__accomplished by considering**the**limit**as**ε → 0**;**but**the**" infinitesimal " language generalizes directly**to**Lie groups over general rings**.**__Formally__

**,**

**a**profinite group

__is__

**a**Hausdorff

**,**compact

**,**

**and**totally disconnected topological group: that

__is__

**,**

**a**topological group that

__is__also

**a**Stone space

**.**

__Formally__

**,**this sharing

**of**dynamics

__is__referred

**to**

**as**universality

**,**

**and**systems

**with**precisely

**the**same critical exponents are said

**to**belong

**to**

**the**same universality class

**.**

__Formally__

**,**

**a**frame

__is__defined

**to**be

**a**lattice L in which

**finite**meets distribute over arbitrary joins

**,**i

**.**e

**.**every ( even infinite ) subset

Formally and used

**;**Electronics:

__Formally__

**a**fixture in radio shacks

**,**now

__used__

**for**assembly

**and**repair

**of**all sorts

**of**electronic equipment including communication

**,**computer

**,**

**and**home entertainment items

**.**

__Formally__known

**as**Mickleham Grand it

__used__

**to**range

**from**Mount Ridley Road

**to**Crestmont Terrace

**,**but now

**is**connected

**to**

**the**urbanised areas

**of**Craigieburn

**.**

Dick Smith Electronics has also long been known

**for**its " home brand " range**of**electronics which fall under**the**brand name " Dick Smith " (__Formally__called DSE**,****a**commonly__used__abbreviation**of**Dick Smith Electronics ).__Formally__

**,**this meant that

**the**whole peloton finished out

**of**time limits

**,**but

**the**referees understandably

__used__

**a**rule saying that they could give clemency

**to**any group

**of**more than 20 %

**of**

**the**stage's starting riders

**,**officially citing

**the**weather conditions

**as**their reason

**to**do so

**.**

Formally and finite

__Formally__

**,**we start

**with**

**a**category C

**with**

__finite__products ( i

**.**e

**.**C has

**a**terminal object 1

**and**any two objects

**of**C have

**a**product ).

__Formally__

**,**

**the**question

**of**whether

**the**universe

**is**infinite or

__finite__

**is**whether it

**is**an unbounded or bounded metric space

**.**

__Formally__

**,**an iterated function

**system**

**is**

**a**

__finite__

**set**

**of**contraction mappings on

**a**complete metric space

**.**

__Formally__

**,**

**the**game ( coalitional game ) consists

**of**

**a**

__finite__

**set**

**of**players

**,**called

**the**grand coalition

**,**

**and**

**a**characteristic function denotes

**the**power

**set**

**of**.</ ref >

**from**

**the**

**set**

**of**all possible coalitions

**of**players

**to**

**a**

**set**

**of**payments that satisfies

**.**

__Formally__

**,**

**a**

**system**

**is**said

**to**be observable if

**,**

**for**any possible sequence

**of**state

**and**control vectors

**,**

**the**current state can be determined in

__finite__time using only

**the**outputs ( this definition

**is**slanted towards

**the**state space representation ).

__Formally__

**,**we define

**a**bad field

**as**

**a**structure

**of**

**the**form ( K

**,**T ), where K

**is**an algebraically closed field

**and**T

**is**an infinite

**,**proper

**,**distinguished subgroup

**of**K

**,**such that ( K

**,**T )

**is**

**of**

__finite__Morley rank in its full language

**.**

__Formally__

**,**

**a**deterministic

__finite__automaton may be defined by

**the**tuple where

**is**

**the**

**set**

**of**states

**of**

**the**automaton

**,**

**is**

**the**

**set**

**of**input

**symbols**

**,**

**is**

**the**transition function that takes

**a**state

**and**an input

**symbol**

**to**

**a**new state

**,**

**is**

**the**initial state

**of**

**the**automaton

**,**

**and**

**is**

**the**

**set**

**of**accepting or final states

**of**

**the**automaton

**.**

__Formally__

**,**assuming our intuition

**from**

**the**

__finite__dimensional case carries over into

**the**infinite dimensional setting

**,**

**the**measure should then be equal

**to**

__Formally__

**,**

**the**upper density

**of**

**a**graph G

**is**

**the**infimum

**of**

**the**values α such that

**the**

__finite__subgraphs

**of**G

**with**density α have

**a**bounded number

**of**vertices

**.**

Formally and cover

__Formally__

**,**

**a**vertex

__cover__

**of**

**a**graph G

**is**

**a**

**set**C

**of**vertices such that

**each**edge

**of**G

**is**incident

**to**at least

**one**vertex in C

**.**The

**set**C

**is**said

**to**

__cover__

**the**edges

**of**G

**.**The following figure shows examples

**of**vertex covers in two graphs (

**and**

**the**

**set**C

**is**marked

**with**red ).

0.146 seconds.